High melt strength propylene polymers are known, for example, those described in U.S. Pat. No. 4,916,198. However, these materials tend to be brittle. Various methods have been tried to overcome this problem, such as blending a soft polymer material with a high melt strength polymer material or irradiating a soft polymer starting material, but with limited success. There is still a need for a propylene polymer material that exhibits both high melt strength and softness.